Details

Time bar (total: 11.4s)

sample97.0ms

Algorithm
intervals
Results
35.0ms147×body160valid
13.0ms282×body80nan
12.0ms538×pre80true
7.0ms45×body320valid
3.0ms64×body80valid

simplify103.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
39.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(- (* b b) (* (* 4.0 a) c))
135.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
86.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series397.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
50.0ms
(- (* b b) (* (* 4.0 a) c))
136.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
105.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.4s

Counts
118 → 118
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01952476
14802169
214441861
done50011789

prune354.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.5b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune65.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
0.3b
(/ (* a c) b)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 55
Calls
2 calls:
25.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
18.0ms
(/ (* a c) b)

series60.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
27.0ms
(/ (* a c) b)

simplify984.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (338.0ms)

IterNodesCost
0111818
1314787
21661559
done5001559

prune145.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (* -2.0 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* 2.0 a))
0.4b
(/ (/ (* a c) (sqrt b)) (sqrt b))
0.4b
(/ (* a c) (sqrt b))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
109×times-frac
62×add-exp-log add-cbrt-cube
60×sqrt-prod
50×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×cbrt-undiv div-exp
17×prod-exp cbrt-unprod
13×associate-/r*
12×associate-/l*
10×div-inv
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/l/
1×associate-*r/
Counts
3 → 160
Calls
3 calls:
40.0ms
(/ (* -2.0 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* 2.0 a))
24.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
12.0ms
(/ (* a c) (sqrt b))

series181.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(/ (* -2.0 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* 2.0 a))
49.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
71.0ms
(/ (* a c) (sqrt b))

simplify1.7s

Counts
169 → 169
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02532910
16802375
227171952
done50011927

prune457.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.5b

regimes441.0ms

Accuracy

10.7% (6.4b remaining)

Error of 11.5b against oracle of 5.1b and baseline of 12.3b

bsearch49.0ms

Steps
ItersRangePoint
4
0.3765543169386318
0.509031623797797
0.4445338611362734

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02438
13138
done3138

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.2s8502×body80nan
989.0ms16502×pre80true
751.0ms4786×body160valid
534.0ms1349×body320valid
178.0ms1865×body80valid